Factor. p^2 + 14p + 13 ____

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is p^2 + 14p + 13. Here, the coefficient of p^2 (a) is 1, the coefficient of p (b) is 14, and the constant term (c) is 13.Find Multiplying Numbers: Find two numbers that multiply to the constant term (c) and add up to the coefficient of p (b). We need two numbers that multiply to 13 and add up to 14. The numbers 1 and 13 satisfy these conditions because 1 * 13 = 13 and 1 + 13 = 14.Write Factored Form: Write the factored form using the two numbers found in the previous step. The factored form of the quadratic expression is (p + 1)(p + 13).

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

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p^2 + 14p + 13

Identify Coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is $p^2 + 14p + 13$ . Here, the coefficient of $p^2$ ( $a$ ) is $1$ , the coefficient of $p$ ( $b$ ) is $14$ , and the constant term ( $c$ ) is $13$ .
Find Multiplying Numbers: Find two numbers that multiply to the constant term $c$ and add up to the coefficient of $p$ ( $b$ ). $\newline$ We need two numbers that multiply to $13$ and add up to $14$ . The numbers $1$ and $13$ satisfy these conditions because $1 \times 13 = 13$ and $1 + 13 = 14$ .
Write Factored Form: Write the factored form using the two numbers found in the previous step. $\newline$ The factored form of the quadratic expression is $(p + 1)(p + 13)$ .